Pre-Calculus is the bridge between algebraic reasoning and the deeper language of mathematics used to describe God’s created order. This course strengthens students’ ability to think abstractly, reason functionally, and recognize patterns that govern motion, growth, cycles, and change.
Pre-Calculus equips students with the mathematical tools necessary for Calculus, Physics, Engineering, Economics, and advanced scientific thinking. More than a technical course, it trains students to observe structure, coherence, and intentionality—echoes of a Creator who is consistent, faithful, and precise.
Students will explore functions, trigonometry, vectors, sequences, series, and introductory limits, developing fluency in symbolic manipulation while cultivating wisdom in interpretation and application.
Biblical & Revelate Learning Integration
Order & Faithfulness: Functions and patterns reveal consistency—mirroring God’s unchanging nature.
Truth Through Clarity: Mathematical models train students to distinguish what is true, approximate, or assumed.
Stewardship of Knowledge: Advanced math as preparation for service, leadership, and problem-solving in the world God loves.
Curriculum & Resources
We will use the Thinkwell Precalculus curriculum, featuring:
Professionally produced, concept-driven video instruction
Online interactive practice with immediate feedback
Downloadable e-notes and worksheets (included with subscription)
Optional printed Companion Workbook (price varies by edition)
Supplies:
Thinkwell Precalculus One-Year Online Subscription (≈ $189)
Spiral-bound notebook or binder
Graph paper
Scientific or graphing calculator (TI-84 or equivalent recommended)
Ruler, pencil, eraser
Grading Breakdown
Homework & Practice: 30%
Quizzes: 10%
Unit Tests: 40%
Midterm Exam: 10%
Final Exam: 10%
Classroom Expectations
Log in 5 minutes early with full name displayed
Camera on, face visible, ready to engage
Materials prepared and homework completed before class
Participate respectfully—encouraging clarity, curiosity, and growth
Homework Policy
Pre-Calculus is cumulative and interconnected. Concepts build rapidly, and mastery requires consistent practice. Homework is not optional—it is essential preparation for discussion, application, and assessment.
Course Outline (32 Weeks)
Weeks 1–4: Functions & Mathematical Modeling
Review of algebraic foundations
Function notation and evaluation
Domain and range
Graphical, numerical, and analytical representations
Transformations of functions
Inverse functions and composition
Weeks 5–8: Polynomial & Rational Functions
Polynomial behavior and end behavior
Factoring and zeros
Rational functions and asymptotes
Graphing techniques
Modeling real-world behavior
Weeks 9–12: Exponential & Logarithmic Functions
Exponential growth and decay
Logarithmic functions and properties
Solving exponential and logarithmic equations
Applications in finance, population, and science
Weeks 13–18: Trigonometry
Angles and radian measure
Unit circle and trigonometric functions
Graphs of sine, cosine, and tangent
Trigonometric identities
Solving trigonometric equations
Law of Sines and Law of Cosines
Applications of trigonometry
Weeks 19–22: Analytic Trigonometry & Vectors
Advanced identities and proofs
Polar coordinates
Vectors in two dimensions
Dot product and vector applications
Weeks 23–26: Sequences, Series & Mathematical Patterns
Arithmetic and geometric sequences
Series and summation notation
Recursive definitions
Mathematical induction (introductory)
Weeks 27–30: Introductory Limits & Conceptual Calculus Readiness
Intuitive understanding of limits
Rates of change
Average vs instantaneous change
Preparing the conceptual ground for Calculus
Weeks 31–32: Review & Integration
Cumulative review and synthesis
Projects connecting Pre-Calculus to physics, creation patterns, or real-world systems
Midterm and final exam preparation
Outcome
By the end of this course, students will be confident, fluent, and prepared—not only for Calculus, but for thoughtful engagement with the structured beauty of the world God has made.